“is” operator behaves unexpectedly with integers

Why does the following behave unexpectedly in Python?

>>> a = 256
>>> b = 256
>>> a is b
True           # This is an expected result
>>> a = 257
>>> b = 257
>>> a is b
False          # What happened here? Why is this False?
>>> 257 is 257
True           # Yet the literal numbers compare properly

I am using Python 2.5.2. Trying some different versions of Python, it appears that Python 2.3.3 shows the above behaviour between 99 and 100.

Based on the above, I can hypothesize that Python is internally implemented such that “small” integers are stored in a different way than larger integers and the is operator can tell the difference. Why the leaky abstraction? What is a better way of comparing two arbitrary objects to see whether they are the same when I don’t know in advance whether they are numbers or not?

Take a look at this:

>>> a = 256
>>> b = 256
>>> id(a)
9987148
>>> id(b)
9987148
>>> a = 257
>>> b = 257
>>> id(a)
11662816
>>> id(b)
11662828

Here’s what I found in the Python 2 documentation, “Plain Integer Objects” (It’s the same for Python 3):

The current implementation keeps an
array of integer objects for all
integers between -5 and 256, when you
create an int in that range you
actually just get back a reference to
the existing object. So it should be
possible to change the value of 1. I
suspect the behaviour of Python in
this case is undefined. 🙂